Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design

Deconvolution of calorimeter response from electrical signals for extracting kinetic data

“…In many cases, the order is usually taken between 1 and 3 because higher values tend to considerably increase the level of noise [10]. To solve this problem, several numerical treatments can be applied, such as z-transform or Nyquist theorem for frequency signals [14,15]. In the software developed in this study a moving median filter was applied [16].…”

On the Use of Online Reparametrization in Automated Platforms for Kinetic Model Identification

“…Let matrix U be the orthonormal basis of right eigenvectors of Hj G¼G P . Matrices Λ and U respectively quantify the extent of the sloppiness and the directions of the parameter space that are associated to the sloppiness [9]. A family of secondary transformation updates G S is built from G P , U, and Λ as in Eq.…”

“…Regularization involves the introduction of a bias in the parameter estimates with the aim of reducing their variance and, concomitantly, reducing the condition number of the problem [10]. Popular regularization techniques are i) the Tikhonov regularization [12,13], ii) the truncated singular value decomposition [9,12], and iii) the parameter subset selection [9,11,12]. Other studies recommend the use of reparametrization (RP) to address the practical identifiability problem of sloppy models [14 -19].…”

Process Modeling, Simulation and Optimization: From Single Solutions to a Multitude of Solutions to Support Decision Making

“…Model validation and adjustment is still a challenging task, since it depends on many aspects like weighting of measured data, often unclear expected accuracy of plant measurements and the identifiability of model parameters . Analytics of intermediate streams might sometimes be more like a trend indicator for plant operation than realistic values, which makes it difficult to define a required measure of agreement to be achieved.…”

“…With respect to modeling, model‐based design of experiments (DoE) plays a significant role and will gain increasing importance. Here especially the question about parameter identifiability is decisive which has been addressed by several authors (e.g., , ). There is the potential to automatize model parameter estimation and design of experiments by using the same procedure as indicated in Fig.…”